Objective. Retinal prostheses evoke visual precepts by electrically stimulating functioning cells in the retina. Despite high variance in perceptual thresholds across subjects, among electrodes within a subject, and over time, retinal prosthesis users must undergo `system fitting', a process performed to calibrate stimulation parameters according to the subject's perceptual thresholds. Although previous work has identified electrode-retina distance and impedance as key factors affecting thresholds, an accurate predictive model is still lacking. Approach. To address these challenges, we 1) fitted machine learning (ML) models to a large longitudinal dataset with the goal of predicting individual electrode thresholds and deactivation as a function of stimulus, electrode, and clinical parameters (`predictors') and 2) leveraged explainable artificial intelligence (XAI) to reveal which of these predictors were most important. Main results. Our models accounted for up to 76% of the perceptual threshold response variance and enabled predictions of whether an electrode was deactivated in a given trial with F1 and AUC scores of up to 0.730 and 0.910, respectively. Our models identified novel predictors of perceptual sensitivity, including subject age, time since blindness onset, and electrode-fovea distance. Significance. Our results demonstrate that routinely collected clinical measures and a single session of system fitting might be sufficient to inform an XAI-based threshold prediction strategy, which has the potential to transform clinical practice in predicting visual outcomes.